Bettina Eick has written an article "Some new simple Lie algebras in characteristic $2$" (www.icm.tu-bs.de/~beick/publ/simlie.pdf‎), with several examples and references for Hamiltonian type simple modular Lie algebras over GF(2), see the table in section $5.3$. It contains $P(1,2)$, $P(1,1,1,1)$, $P(2,1,1)$, $P(3,1)$, $P(2,2)$ etc.. For interpretations of these simple modular Lie algebras of Cartan type, see also the book(s) of Helmut Strade.

Bettina Eick has written an article "Some new simple Lie algebras in characteristic $2$" (www.icm.tu-bs.de/~beick/publ/simlie.pdf‎), with several examples and references for Hamiltonian type simple modular Lie algebras over GF(2), see the table in section $5.3$. It contains $P(1,2)$, $P(1,1,1,1)$, $P(2,1,1)$, $P(3,1)$, $P(2,2)$, etc. A further reference is L. Lin, "Nonalternating Hamiltonian algebra $P (n, m)$ of characteristic two". For interpretations of simple modular Lie algebras of Cartan type in general, see also the book(s) and survey articles of Helmut Strade.